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Proceedings of the Royal Society of Edinburgh, Volume 8
Royal Society of Edinburgh
Volledige weergave - 1875
Proceedings of the Royal Society of Edinburgh, Volume 6
Royal Society of Edinburgh
Volledige weergave - 1869
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Pagina 6 - I desire to express my thanks to the Executive Committee of the Carnegie Trust for the Universities of Scotland, for a grant to defray the expenses of this research.
Pagina 400 - Let f, f be the displacement-components of any particle of the water whose undisturbed position is (x, z). We suppose the disturbance infinitesimal; by which we mean that the change of distance between any two particles of water is infinitely small in comparison with their undisturbed distance ; and that the line joining them experiences changes of direction which are infinitely small in comparison with the radian.
Pagina 141 - ... forms of the surface of this obstacle, each encounter will introduce a disturbance into the motion of the system, so that it will pass from one undisturbed path into another. The two paths must both satisfy the equation of energy, and they must intersect each other in the phase for which the conditions of encounter with the fixed obstacle are satisfied, but they are not subject to the equations of momentum. It is difficult in a case of such extreme complexity to arrive at a thoroughly satisfactory...
Pagina 289 - ... from front to back — the uniformity in cranial type all through the British Isles is so perfect that it can not be represented by shaded maps as we have heretofore been accustomed to do. Wherever heads have been measured, whether in the Aran Islands off the west coast of Ireland, the Hebrides and Scottish Highlands, Wales and Cornwall, or the counties about London, the results all agree within a few units. These figures, noted upon the localities where they were taken, are shown upon our little...
Pagina 140 - The motion of a system not acted on by external forces satisfies six equations besides the equation of energy, so that the system cannot pass through those phases, which, though they satisfy the equation of energy, do not also satisfy these six equations. Again, there may be particular laws of force, as for instance that according to which the stress between two particles is proportional to the distance between them, for which the whole motion repeats itself after a finite time. In such cases a particular...
Pagina 406 - The formulas are simplified by taking g = 4. This is merely equivalent to taking as our unit of length half the space descended in one second of time, by a body falling from rest under the influence of gravity. For simplification in the writing of formulas we take z = 1 for the undisturbed level of the water-surface. The subsidiary curves, explained in § 107 below, are called argumentcurves, as they represent the argument of the cosine in (144). 106. One exceedingly curious and very interesting...
Pagina 140 - The only assumption which is necessary for the direct proof is that the system, if left to itself in its actual state of motion, will sooner or later pass through every phase which is consistent with the equation of energy.
Pagina 435 - This allows us to neglect o> in the arguments of E in (205), (206), and makes P and Q constant relatively to t. § 157. When t is small or large, and x not so small as to give preponderance to the first terms of the moduluses (209), (210), we have in (205), (206), (189), (190) a full representation of the whole circumstances of the wave-front, extending from...
Pagina 541 - H, the proposition at which we have just arrived would lead us to believe that each atom of hydrogen does not remain quietly in juxtaposition with the atom of chlorine with which it first united, but, on the contrary, is constantly changing places with other atoms of hydrogen, or, what is the same thing, changing chlorine.
Pagina 400 - F (#, z, t) is what is commonly called the velocitypotential. Thus a knowledge of the function F, for all values of x, z, t, completely defines the displacement and the velocity of the fluid. And towards the determination of F we have, in virtue of the incompressibility of the fluid, <->• In virtue of this equation, the well-known primary theory of Gauss and Green shows that, if F is given for every point of the free surface of the water, and is zero at every point infinitely distant from it the...